Solving dynamic system of equations with parameters

Hello,

I would like to solve a system of equations with parameters. An example (with trivial math) is attached. The system and the variables I would like to solve it for are dependent on a user input. In my example that is the varialbe "length" which can take an arbitrary positive natural number.

I can solve it by explicitly listing the variables "a(1)", etc. in the solve function call. Since the varialbe vector "a" is userdependent I cant use that in general though.

The second function call to solve results in warnings and wrong answers, because solve assumes that the second input "a" is an equation array and not the variables to be solved for.

Any suggestions to solve the system for, say, a random (positive and natural number) "length"?

Thanks a lot in advance!

length = 3;

a = sym('a', [length, 1]);
equations = sym('something', [length, 1]);
syms p

for runIdx = 1:length
    equations(runIdx) = a(runIdx) - p == 0;
end

answers_correct_but_static = solve(equations, a(1), a(2), a(3))

answers_incorrect_dynamic = solve(equations, a)

Answer 1

[A Jenkins]

Due to the way solve choses the variables to solve for ( symvar ), you may not need to specify the variables at all. For example, if you use 'x' as your variable name instead of 'a', this works in 2013b:

length = 3;
x = sym('x', [length, 1]);
equations = sym('something', [length, 1]);
syms p
for runIdx = 1:length
    equations(runIdx) = x(runIdx) - p == 0;
end
answers_correct_dynamic = solve(equations)

[Sebastian]

Hugh. Your suggestion works indeed.

I'm still confused though. I was aware of the fact that solve uses symvar to select the variables to solve for. Hence I used "a" as the variable name, because I figured it is selected first from symvar. Simply calling

    answers = solve(equations);

In my above example doesn't work though.. How comes symvar picks the x's over the p? Or in other words: How robust is this solution?

[A Jenkins]

Try this:

symvar(equations,length)

The documentation says it prefers variables "alphabetically closest to x."

http://www.mathworks.com/help/symbolic/symvar.html

Someone from TMW would have to comment on robustness, but I guess I agree that it seems natural to me that if you aren't sure, x,y,z are a good guess for variables and a,b,c are usually some kind of constant.